A088867 -id:A088867 - cp's OEIS frontend

A230562 Smallest number that is the sum of 2 positive 4th powers in >= n ways.

0, 2, 635318657

Offset: 0

Jonathan Sondow, Oct 25 2013

Hardy and Wright say that a(3) is unknown.

Guy, 2004: "Euler knew that 635318657 = 133^4 + 134^4 = 59^4 + 158^4, and Leech showed this to be the smallest example. No one knows of three such equal sums."

			0 = (empty sum).
2 = 1^4 + 1^4.
635318657 = 59^4 + 158^4 = 133^4 + 134^4.

R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, D1
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 6th edition, 2008; section 21.11.

Carlos Rivera, Puzzle 103: N = a^4 + b^4 = c^4 + d^4

Cf. A003824, A016078, A018786, A046881, A088687, A088848, A088849, A088867, A230561.

A088665 q such that p^4 + q^4 = r^4 + s^4 = a(n).

Original entry on oeis.org

59, 7, 193, 271, 103, 222, 76, 878, 1324, 1042, 248, 1034, 1577, 1623, 661, 3364, 2694, 604, 2027, 274, 2707, 498, 1259, 5181, 1657, 6262, 4903, 5098, 635, 1104, 1142, 173, 5452, 3401, 5277, 3779, 3644, 2903, 1525, 1149, 5121, 5526, 6470, 6496, 261, 581

Offset: 1

Cino Hilliard, Nov 23 2003

D. J. Bernstein, List of 516 primitive solutions p^4 + q^4 = r^4 + s^4

Cf. A003824, A088728, A088867.

cp's OEIS Frontend

A230562 Smallest number that is the sum of 2 positive 4th powers in >= n ways.

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